from the palace, after ordering the rival protesters to pull back.
And in Morsi's hometown, the Nile Delta city of Zagazig, police used tear gas to disperse protesters who surrounded the home of one of the president's relatives, a police official said.
On Wednesday night, five people were killed and 644 injured that pitted Islamists against an opposition that has escalated protests since Morsi issued a decree two weeks ago assuming sweeping powers.
Many demonstrators were injured by birdshot, the health ministry said, but it was not immediately clear who was firing.
Early on Thursday, intermittent gunshots rang out amid sporadic violence, before the Republican Guard, whose job is to protect the presidency, deployed troops and at least 10 tanks outside the palace.
Morsi supporters who had camped out there began packing their belongings after a military ultimatum for them to leave by 3:00pm (1300 GMT).
Anti-Morsi protesters were also pushed back.
Republican Guard chief General Mohammed Zaki said the tanks were deployed to separate the warring sides, pledging that the military "will not be an instrument of oppression."
The opposition has said it would organise further marches to the palace. Morsi, who often spends the night at his private home in another Cairo suburb, arrived at the palace early on Thursday.
Egypt's top Islamic body, Al-Azjar, told Morsi he should "suspend the latest decree and stop using it," while also demanding an unconditional dialogue between the president and his opponents.
A senior aide said the president, elected in June, was expected to deliver a televised address to the nation later in the day reaching out to the opposition.
Four of Morsi's advisers have resigned over the crisis, official news agency MENA reported, and the head of state television has also quit, the independent newspaper Al-Masry al-Youm reported on its website.
The stage was set for Wednesday's violence when the Muslim Brotherhood, from which Morsi comes, announced a march to the palace where opposition protesters were holding a sit-in.
Protesters fired guns and threw fire bombs and rocks at each other as their simmering stand-off over Morsi's expanded powers and a controversial draft constitution turned violent.
The opposition says it will not stand down until Morsi discards his new powers -- which allow him to take decisions uncontested by the courts -- and until he cancels a snap December 15 referendum on the new constitution opposed by liberals and Christians.
The Brotherhood urged protesters on both sides to withdraw, as did Prime Minister Hisham Qandil.
The United States has called for an open and "democratic dialogue" in Egypt.
"The upheaval we are seeing... indicates that dialogue is urgently needed. It needs to be two-way," US secretary of state Hillary Clinton said in comments echoed by Britain and the European Union.
Despite the protests, vice president Mahmud Mekki said a referendum on the charter "will go ahead on time" on December 15.
He said the opposition would be allowed to put any objections to articles in the draft constitution in writing, to be discussed by a parliament yet to be elected.
Prominent opposition leader and former UN nuclear watchdog chief Mohamed ElBaradei said Morsi bore "full responsibility" for the violence.
He said the opposition was ready for dialogue but would use "any means necessary" to scupper the charter, stressing, however, that these would be peaceful.